Probability: Modeling and Applications to Random Processes

To the Student.

To the Instructor.

Coverage.

Acknowledgments.

Chapter 1. Modeling.

1.1  Choice and Chance.

1.2  The Model Building Process.

1.3  Modeling in the Mathematical Sciences.

1.4  A First Look at a Probability Model: The Random Walk.

1.5  Brief Applications of Random Walks.

Exercises.

Chapter 2.  Sets and Functions.

2.1  Operations with Sets.

2.2  Functions.

2.3  The Probability Function and the Axioms of Probability.

2.4  Equally Likely Sample Spaces and Counting Rules.

Rules.

Exercises.

Chapter 3.  Probility Laws I: Building on the Axioms.

3.1  The Complement Rule.

3.2  The Addition Rule.

3.3  Extensions and Additional Results.

Exercises.

Chapter 4.  Probility Laws II: Results of Conditioning.

4.1  Conditional Probability and the Multiplication Rule.

4.2  Independent Events.

4.3  The Theorem of Total Probabilities and Bayes' Rule.

4.4  Problems of Special Interest: Effortful Illustrations of the Probability Laws.

Exercises.

Chapter 5.  Random Variables and  Stochastic Processes.

5.1  Roles and Types of Random Variables.

5.2  Expectation.

5.3  Roles, Types, and Characteristics of  Stochastic Processes.

Exercises.

Chapter 6.  Discrete Random Variables and Applications in Stochastic Processes.

6.1  The Bernoulli and Binomial Models.

6.2  The Hypergeometric Model.

6.3  The Poisson Model.

6.4  The Geometric and Negative Binomial.

Models.

Exercises.

Chapter 7.  Continuous Random Variables and Applications in Stochastic Processes.

7.1  The Continuous Uniform Model.

7.2  The Exponential Model.

7.3  The Gamma Model.

7.4  The Normal Model.

Chapter 8.  Covariance and Correlation Among Random Variables.

8.1  Joint, Marginal and Conditional Distributions.

8.2  Covariance and Correlation.

8.3  Brief  Examples and Illustrations in Stochastic Processes and Times Series.

Exercises.

Bibliography.

Tables.

Index.